Question 1

An electron is trapped in a deep well with a width of 0.3 nm. If it is in the state with quantum number n = 3 its kinetic energy is:

Accepted Answer

A)  6.0 * 10-28 J 
B)  1.8 *10-27 J 
C)  6.7 * 10-19 J 
D)  2.0 *10-18 J 
E)  6.0*10-18 J 
A)  6.0 * 10-28 J 
B)  1.8 *10-27 J 
C)  6.7 * 10-19 J 
D)  2.0 *10-18 J 
E)  6.0*10-18 J E

Question 2

The ground state energy of an electron in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls:

Accepted Answer

A)  is zero 
B)  decreases with temperature 
C)  increases with temperature 
D)  is independent of temperature 
E)  oscillates with time 
A)  is zero 
B)  decreases with temperature 
C)  increases with temperature 
D)  is independent of temperature 
E)  oscillates with time D

Question 3

An electron in an atom initially has an energy 7.5 eV above the ground state energy. It drops to a state with an energy of 3.2 eV above the ground state energy and emits a photon in the process. The momentum of the photon is:

Accepted Answer

A)  1.7 * 10-27 kg .m/s 
B)  2.3 *10-27 kg . m/s 
C)  4.0 * 10-27 kg . m/s 
D)  5.7 * 10-27 kg .m/s 
E)  8.0 * 10-27 kg . m/s 
A)  1.7 * 10-27 kg .m/s 
B)  2.3 *10-27 kg . m/s 
C)  4.0 * 10-27 kg . m/s 
D)  5.7 * 10-27 kg .m/s 
E)  8.0 * 10-27 kg . m/s B

Question 4

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and porton. Then the ground state energy of a hydrogen atom is -13.6 eV. The minus sign indicates:

Accepted Answer

A)  the kinetic energy is negative 
B)  the potential energy is positive 
C)  the electron might escape from the atom 
D)  the electron and proton are bound together 
E)  none of the above 
A)  the kinetic energy is negative 
B)  the potential energy is positive 
C)  the electron might escape from the atom 
D)  the electron and proton are bound together 
E)  none of the above

Question 5

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and porton. Then the ground state energy of a hydrogen atom is -13.6 eV. When the electron is in the first excited state the ionization energy is:

Accepted Answer

A)  0 
B)  3.4 eV 
C)  6.8 eV 
D)  10.2 eV 
E)  13.6 eV 
A)  0 
B)  3.4 eV 
C)  6.8 eV 
D)  10.2 eV 
E)  13.6 eV

Question 6

Which of the following sets of quantum numbers is possible for an electron in a hydogen atom?

Accepted Answer

A)  n = 4,     
B)  n = 4,     
C)  n = 5,     
D)  n = 3,     
E)  n = 2,     
A)  n = 4,     
B)  n = 4,     
C)  n = 5,     
D)  n = 3,     
E)  n = 2,

Question 7

An electron in an atom initially has an energy 5.5 eV above the ground state energy. It drops to a state with energy 3.2 eV above the ground state energy and emits a photon in the process. The wave associated with the photon has a wavelength of:

Accepted Answer

A)  5.4 *10 - 7 m 
B)  3.0 *10 - 7 m 
C)  1.7 *- 7 m 
D)  1.15 * 10 - 7 m 
E)  1.0 *10 - 7 m 
A)  5.4 *10 - 7 m 
B)  3.0 *10 - 7 m 
C)  1.7 *- 7 m 
D)  1.15 * 10 - 7 m 
E)  1.0 *10 - 7 m

Question 8

Consider the following:   Of these which are spherically symmetric?

Accepted Answer

A)  only I 
B)  only II 
C)  only I and II 
D)  only I and III 
E)  I, II, and III 
A)  only I 
B)  only II 
C)  only I and II 
D)  only I and III 
E)  I, II, and III

Question 9

Take the potential energy of a hydrogen atom to be zero for infinite seperation of the electron and proton. Then, according to the quantum theory the energy En of a state with principal quantum number n is proportional to:

Accepted Answer

A)  n 
B)  n2 
C)  1/n 
D)  1/n2 
E)  none of the above 
A)  n 
B)  n2 
C)  1/n 
D)  1/n2 
E)  none of the above

Question 10

A particle is trapped in an infinite potential energy well. It is in the state with quantum number n = 14. How many nodes does the probability density have (counting the nodes at the ends of the well)?

Accepted Answer

A)  none 
B)  7 
C)  13 
D)  14 
E)  15 
A)  none 
B)  7 
C)  13 
D)  14 
E)  15

Question 11

The principle of complementarity is due to:

Accepted Answer

A)  Einstein 
B)  Maxwell 
C)  Newton 
D)  Bohr 
E)  Schrodinger 
A)  Einstein 
B)  Maxwell 
C)  Newton 
D)  Bohr 
E)  Schrodinger

Question 12

An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls. A graph of its wave function $\Psi$(x) versus x is shown. The value of quantum number n is:

Accepted Answer

A)  0 
B)  1 
C)  4 
D)  6 
E)  8 
A)  0 
B)  1 
C)  4 
D)  6 
E)  8

Question 13

A particle in a certain finite potential energy well can have any of five quantized energy values and no more. Which of the following would allow it to have any of six quantized energy levels?

Accepted Answer

A)  Increase the momentum of the particle 
B)  Decrease the momentum of the particle 
C)  Decrease the well width 
D)  Increase the well depth 
E)  Decrease the well depth 
A)  Increase the momentum of the particle 
B)  Decrease the momentum of the particle 
C)  Decrease the well width 
D)  Increase the well depth 
E)  Decrease the well depth

Question 14

A particle is trapped in an infinite potential energy well. It is in the state with quantum number n = 14. How many maxima does the probability density have?

Accepted Answer

A)  none 
B)  7 
C)  13 
D)  14 
E)  15 
A)  none 
B)  7 
C)  13 
D)  14 
E)  15

Question 15

An electron in an atom drops from an energy level at -1.1 * 10-18 J to an energy level at -2.4 * 10-18 J. The wave associated with the emitted photon has a frequency of:

Accepted Answer

A)  2.0* 1017 Hz 
B)  2.0 * 1015 Hz 
C)  2.0 *1013 Hz 
D)  2.0 * 1011 Hz 
E)  2.0 * 109 Hz 
A)  2.0* 1017 Hz 
B)  2.0 * 1015 Hz 
C)  2.0 *1013 Hz 
D)  2.0 * 1011 Hz 
E)  2.0 * 109 Hz

Question 16

The Balmer series of hydrogen is important because it:

Accepted Answer

A)  is the only one for which the Bohr theory can be used 
B)  is the only series which occurs for hydrogen 
C)  is in the visible region 
D)  involves the lowest possible quantum number n 
E)  involves the highest possible quantum number n 
A)  is the only one for which the Bohr theory can be used 
B)  is the only series which occurs for hydrogen 
C)  is in the visible region 
D)  involves the lowest possible quantum number n 
E)  involves the highest possible quantum number n

Question 17

The energy of a particle in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls is proportional to (n = quantum number):

Accepted Answer

A)  n 
B)  1/n 
C)  1/n2 
D)    
E)  n2 
A)  n 
B)  1/n 
C)  1/n2 
D)    
E)  n2

Question 18

Two one-dimensional traps have infinite potential energy at their walls. Trap A has width L and trap B has width 2L. For which value of the quantum number n does a particle in trap B have the same energy as a particle in the ground state of trap A?

Accepted Answer

A)  n = 1 
B)  n = 2 
C)  n = 3 
D)  n = 4 
E)  n = 5 
A)  n = 1 
B)  n = 2 
C)  n = 3 
D)  n = 4 
E)  n = 5

Question 19

The diagram shows the energy levels for an electron in a certain atom. Of the transitions shown, which represents the emission of a photon with the most energy?

Accepted Answer

A)  I 
B)  II 
C)  III 
D)  IV 
E)  V 
A)  I 
B)  II 
C)  III 
D)  IV 
E)  V

Question 20

The series limit for the Balmer series represents a transition m $\rightarrow$ n, where (m, n) is

Accepted Answer

A)  (2,1) 
B)  (3,2) 
C)  ($\infty$,0) 
D)  ($\infty$,1) 
E)  ($\infty$,2) 
A)  (2,1) 
B)  (3,2) 
C)  ($\infty$,0) 
D)  ($\infty$,1) 
E)  ($\infty$,2)

Exam 39: More About Matter Waves

An electron is trapped in a deep well with a width of 0.3 nm. If it is in the state with quantum number n = 3 its kinetic energy is:

The ground state energy of an electron in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls:

An electron in an atom initially has an energy 7.5 eV above the ground state energy. It drops to a state with an energy of 3.2 eV above the ground state energy and emits a photon in the process. The momentum of the photon is:

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and porton. Then the ground state energy of a hydrogen atom is -13.6 eV. The minus sign indicates:

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and porton. Then the ground state energy of a hydrogen atom is -13.6 eV. When the electron is in the first excited state the ionization energy is:

Which of the following sets of quantum numbers is possible for an electron in a hydogen atom?

An electron in an atom initially has an energy 5.5 eV above the ground state energy. It drops to a state with energy 3.2 eV above the ground state energy and emits a photon in the process. The wave associated with the photon has a wavelength of:

Consider the following: Of these which are spherically symmetric?

Take the potential energy of a hydrogen atom to be zero for infinite seperation of the electron and proton. Then, according to the quantum theory the energy En of a state with principal quantum number n is proportional to:

A particle is trapped in an infinite potential energy well. It is in the state with quantum number n = 14. How many nodes does the probability density have (counting the nodes at the ends of the well)?

The principle of complementarity is due to:

An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls. A graph of its wave function Ψ\PsiΨ (x) versus x is shown. The value of quantum number n is:

A particle in a certain finite potential energy well can have any of five quantized energy values and no more. Which of the following would allow it to have any of six quantized energy levels?

A particle is trapped in an infinite potential energy well. It is in the state with quantum number n = 14. How many maxima does the probability density have?

An electron in an atom drops from an energy level at -1.1 * 10-18 J to an energy level at -2.4 * 10-18 J. The wave associated with the emitted photon has a frequency of:

The Balmer series of hydrogen is important because it:

The energy of a particle in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls is proportional to (n = quantum number):

Two one-dimensional traps have infinite potential energy at their walls. Trap A has width L and trap B has width 2L. For which value of the quantum number n does a particle in trap B have the same energy as a particle in the ground state of trap A?

The diagram shows the energy levels for an electron in a certain atom. Of the transitions shown, which represents the emission of a photon with the most energy?

The series limit for the Balmer series represents a transition m →\rightarrow→ n, where (m, n) is

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Take the potential energy of a hydrogen atom to be zero for infinite seperation of the electron and proton. Then, according to the quantum theory the energy E_n of a state with principal quantum number n is proportional to:

An electron in an atom drops from an energy level at -1.1 * 10^-¹⁸ J to an energy level at -2.4 * 10^-¹⁸ J. The wave associated with the emitted photon has a frequency of:

The series limit for the Balmer series represents a transition m $\rightarrow$ n, where (m, n) is